Need help to create this equation
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Hi everyone, I am a little bit confused about this
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/495438/image.png)
Could someone helping me to create this? It seems that to many partial derivatives, since I am not good at it.
*you can assume the parameter by yourself or let them be in coefficient
Hope someone could help me to understand clearly how to perform this equation. Thankyou very much!
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Walter Roberson
2021년 2월 17일
syms rho_eff_hcp
syms p_w(x,t)
syms w(p_w_)
syms w_r(t)
dw_dp_w = diff(w(p_w_),p_w_)
dp_w_dt = diff(p_w(x,t),t);
LHS = 1/rho_eff_hcp * dw_dp_w * dp_w_dt;
dp_w_dx = diff(p_w(x,t),x)
syms K
RHS_temp1 = K*w(p_w_)*dp_w_dx
RHS_temp2 = diff(RHS_temp1,x)
dw_r_dt = diff(w_r(t),t);
RHS = -RHS_temp2 + dw_r_dt;
eqn = LHS == RHS
Now you are faced with the problem that w should be a function of p_w instead of p_w_ but p_w is a function. You are trying to take the derivative of a function with respect to a function, which requires Calculus of Variations instead of regular calculas.
You also have three functions but only one equation. There is no hope that you would be able to resolve this symbolically, even if the equations were ODE instead of PDE.
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Bjorn Gustavsson
2021년 2월 18일
No, it doesn't look right. When you write your C-N function you will get to a stage where you have to multiply the RHS with the inverse of the LHS-matrix. You have neither an inv nor a \ in your C-N section. Take a pen and paper, sit down and write out the expressions for the LSH and RHS matrices and then implement those expressions. You will get a step looking something lke this:
I_next = invMLHS*([Mrhs]*I_prev + Q_t_p_half);
HTH
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